It's awesome that you care enough about your fish to be here asking these questions. Many people don't. On that note, I hope you realize that what follows in this post is not intended to do anything except clear up where you feel that you have been given opposing information.
Prime will detoxify ammonia and nitrites, but they will still show up on tests, and they still feed bacteria. I would definately use it and stability asap. Stability will ADD the bacteria to help your cycle!
nitrites change when you do a water change, but don't indicate a change because:
your reagent is faulty,
or, more likely,
you are at over double the max indicated on nitrites before you do your water change.
You shouldn't do water changes during your cycle. You should cycle w/o fish. Sense you wound up cycling with fish, you must do many waterchanges or they will die.
Large water changes can be a problem. BUT only if your fish have not had a waterchange in a long time. If you routinely change your water, you could do 75% twice a day, and it wouldn't cause problems.
A POSSIBLE cause of high nitrites: a dead fish. I've been told in the past that although ammo, ites, and ates are all products of decomposition, certain forms of decomp produce more of one than the others. to me, this makes sense. I've been told that a dead fish left in a tank can cause a nitrite spike, w/o greatly affecting ammo or ates. Obviously, over time your bact colonies will grow, consume the ites, and convert them to ates. Your plants will consume both, and water changes will remove both. So, what I am trying to say, abbreviated, is: A dead fish that you have not found may be causing your nitrite spike.
So, the abriged version of this post:
I reccomend dosing prime and stability ASAP.
I reccomend testing your water, doing a 50% water change, immediately testing your water, if still above .25ppm ites, doing a 50% water change, immediately testing your water, it still above .25 ppm ites, rinse and repeat. Do this until you indicate less than .25 ppm nitrites. BUT make sure your water is conditioned with dechlorinator, and that it is the same temp as your tank water before adding it.